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Zarkon

6 years ago

Start with this...suppose \(A\) is \(m\times n\) and \(B\) is \(n\times k\)
Let \(\mathbf{b}_1,\mathbf{b}_2,\ldots \mathbf{b}_k\) be the column vectors of \(B\)
since they are L.D. then there is a nontrivial solution to
\[c_1\mathbf{b}_1+c_2\mathbf{b}_2+\cdots+c_k\mathbf{b}_k=0\]
write out what \(AB\) would be in terms of the column vectors of B...